Three master CFI's recorded a recent webinar on this topic. It's a VERY good listen. The webinar was done for the Society of Aviation and Flight Educators (SAFE). Good advice, good analysis, very good cautionary statements. I personally know at least one pilot who is still alive because he did exactly as was suggested in this excellent webinar: On takeoff from a back country strip choices were limited to to "fly straight ahead" and hit a cliff or 'land' in 100' trees, or make the turn and set down in an opening created by recent logging. He survived the resulting crash because (a) he was under control and making a 3 point full stall landing until the moment one wing hit the only d*** tree in the opening and spun his aircraft; (b) he and his wife were wearing 4 point harnesses (snugged before takeoff); and (c) he was fortunate enough to have several friends see the crash and IMMEDIATELY respond. There's no doubt the outcome would have been fatal had he made any other choice. My friend is a very good pilot, pre-brief's his takeoffs, and pre-briefs his options. How many of us do that EVERY TIME?

FWIW, engine failure is not common, but it occurs more often that the NTSB accident db shows. Based on a survey of over 1000 pilots, 170 of whom reported one or more power loss events in single engine, piston powered, fixed wing, production aircraft about 1 in 6 pilots are likely to have to use their emergency off airport or 'improbable return' skills. The cheerful news is only about 1 in 15 of the survey pilots experienced an accident. However, data are incomplete. Dead pilots don't respond to post event surveys. Practice emergency procedures, and unless the decision is premade and skills recently practiced realize that "improbable" becomes pretty darn close to "impossible" for that maneuver.

I sat through a very informative presentation my Michael Church, reference my Rod in this video, at Oshkosh last summer entitled "The Possible Turn". Michael showed videos of turn back tests done with 30,45 and 60 degrees of bank. Michael basically made the argument that if you have sufficient altitude, and proficiency, he recommends rolling to 60 degrees of bank and pulling to the buffet for the entire turn. I've started adding this to my personal proficiency flying and instruction I give during recurrent training ( I'm not comfortable teaching this to student pilots), and it's very impressive how quickly you can get a 172 or 182 turned around if you have to.

...Michael showed videos of turn back tests done with 30,45 and 60 degrees of bank. Michael basically made the argument that if you have sufficient altitude, and proficiency, he recommends rolling to 60 degrees of bank and pulling to the buffet for the entire turn. ...

Michael's points about proficiency are the first and second of the three ingredients to a successful outcome to the improbable turn. I agree it's VERY impressive how rapidly an aircraft will turn at slow airspeeds and steep bank angles. I think with a face full of ground it would be WAY too easy to pull back 'just a little' to streeeettttccccchhhhhhh that glide. There are certainly places where an aggressive return maneuver would be the 'best option'. For example, 'system malfunction - powerplant' during a takeoff from an airport surrounded by a sea of densely packed buildings. North Las Vegas, San Diego's Gillespie Field, Santa Monica, and several others come to mind. The third ingredient of a successful turn back is a pre-planned takeoff so we know with certainty that we'll achieve a survivable outcome. IMHO, the implied argument in favor of the improbable turn in the AOPA's online video https://www.youtube.com/watch?v=F-C5E9qj52w is it was necessary to 'save the aircraft'. I disagree with that premise. When the engine quits or malfunctions so insufficient power is produced the PIC has just TWO priorities: (1) Protecting the cockpit and minimizing risks of fatalities or serious injuries to aircraft occupants AND (2) avoiding death or serious injuries to persons on the ground. The aircraft belongs to the insurance company...

I agree completely with all of your points. Our squadron happens to be based at an airport surrounded by densely packed buildings making engine failure during a southern take off very difficult to survive if were forced to land straight ahead. Personally I used to brief this take off with a decision altitude for turn back at 1,000 AGL. After sitting through Michael's presentation, and routinely practicing the maneuver, that decision altitude is now lower. Having said that, at every other airport in our area my pre-flight brief is still to land straight ahead below 1,000 feet as there are plenty of options available straight ahead.